Tracking the Intangible: Quantifying Effort in NFL Running Backs
Image source: The Tower
Introduction
American Football is one of the most-watched and popular sports in the U.S., known for its quick decision-making, complex tactics, and athletically demanding displays of strength, endurance and speed. However, many traditional statistics miss the “how” behind value plays such as yards gained after contact, expected points added, etc. As such, we must ask ourselves: what does it take to gain a yard? Is a player exceeding their capabilities, therefore, making an effort? If so, how often or how close does a player comes to his “best”?
Our motivation for this project centered on these very questions. Our goal is to develop a metric to measure effort. We acknowledge that effort is a complex, intangible, and most often subjective concept, influenced by player position, opposing defense, snap count or play volume to play call/assignment. Effort is also heavily contextual and multi-faceted, often shaped by the emotional and mental state as well as the thinking process of a player. Given the available data, we are going to focus on one facet: the raw physical capabilities of a player — specifically, acceleration and speed.
By quantifying effort, we hope to provide not only to teams and sport data analysts, but also fans with deeper insight into what and how football players are truly contributing on the field — even when it’s not reflected in conventional stats or even the outcome of a game. We also aspire to address or even fill in some of the gaps in the current literature around quantifying effort in American football since most research focus on win probabilities and other outcomes at the game level rather than individualized capabilities.
Data
The data used for this project were the games, plays, players, tracking data sets from the NFL Big Data Bowl 2025, weeks 1-9 on Kaggle (NFL Big Data Bowl 2025).
Data pre-porcessing
- We limited our dataset to NFL running backs with more than 20 rushes per play during the 2022 season.
- We limited the rows to running plays where a running back (RB) is the ball carrier.
- We Trimmed each play to frames between handoff and at end of a play.
Methods
In this project, we define effort as a running back’s ability to consistently reach a combination of their individual maximal acceleration for any given speed.
Metric #1: Linear Regression
Our main methodological approach to addressing this question centered around previous research that has explored soccer players reaching their theoretical max acceleration capacity for every running speed (Morin et al. 2021). Similarly, we adopted this framework by plotting an individual running back’s profile based on the maximal acceleration the running back could generate for every possible running speed as follows:
- Within a speed interval ranging between 3 mph and the RB’s maximal speed, the two maximal acceleration values attained for each 0.2 mph sub-intervals were selected.
- A first linear regression was fit to these speed-acceleration points.
- Outlier points lying outside of 95% confidence interval around the linear function were removed.
- A linear regression was fit to the remaining points.
This effort metric was derived by transforming final regression line downward by 0.25 units.
Effort = percentage of points above the transformed regression line
Linear quantile regression for acceleration(mph/s) vs speed(mph)
Metric #2: Additive Quantile Regression Model
This metric quantifies how often a runnng back comes close to their maximal acceleration capacity.
Assumption of this effort metric: high acceleration and/or high speed movements are effortful.
For each running back, two regression models with adaptive spline bases were fitted to the 0.98 quantiles of positive and negative acceleration, respectively, both as functions of running speed. A vertical line at the 0.99 quantile of speed was also drawn.
This metric was derived by
[LATEX equation]
where di is the shortest distance from each point to its corresponding quantile regression line (either for positive or negative acceleration) or to the vertical line at the 0.99 quantile of speed.
- For points outside the quantile regression lines and/or the vertical line, the distance di was set to 0.
- For negative acceleration points, the effort score[change] was penalized with by a factor of 0.5 as deceleration is deemed less effortful.
Top Running backs
Top 10
Metric #3: Ellipse [this metric might go on the appendix(???)]
- For each running back, an ellipse was plotted with a vertex (x-intercept) at the 99th percentile of speed and co-vertices (y-intercepts) at the 99th percentiles of positive and negative acceleration, respectively.
- This effort metric was derived in the same manner as for the quantile regression above, where di here is the shortest distance from each point to the ellipse.
Results
[Describe your results. This can include tables and plots showing your results, as well as text describing how your models worked and the appropriate interpretations of the relevant output. (Note: Don’t just write out the textbook interpretations of all model coefficients. Instead, interpret the output that is relevant for your question of interest that is framed in the introduction)]]
Discussion
[Give your conclusions and summarize what you have learned with regards to your question of interest. Are there any limitations with the approaches you used? What do you think are the next steps to follow-up your project?]
- AS profile framework didn’t translate into football (maybe it works for other sports where players don’t get tackled but just run at hand-off)
- there are many dependencies in NFL
- this is a productive place to start quantifying effort
- further research should look into taking into account other factors/variables
Appendix
Tab 2: Bottom running backs
Tables
- Percentage of total points that lie in between the percentile P_{99} and P_{99}-3
- This effort metric quantifies how often a player comes close to his “best” (99th percentile) accelerations
Trying a different interactive layout
Acknowledgements
- Used Dr. Ron Yurko and Quang Nguyen’s code to calculate distance from the nearest defender (Nguyen 2023)
- Still using the non-linear quantile regression plot? (Ding 2024)
References
Ding, Peng. 2024. Linear Models and Extensions. Chapman & Hall. https://arxiv.org/pdf/2401.00649.
Morin, Jean-Benoit, Yann Le Mat, Cristian Osgnach, Andrea Barnabò, Alessandro Pilati, Pierre Samozino, and Pietro E. di Prampero. 2021. “Individual Acceleration-Speed Profile in-Situ: A Proof of Concept in Professional Football Players.” Journal of Biomechanics 123: 110524. https://doi.org/https://doi.org/10.1016/j.jbiomech.2021.110524.
NFL Big Data Bowl. 2025. “NFL Big Data Bowl 2025 Dataset.” Kaggle. https://www.kaggle.com/competitions/nfl-big-data-bowl-2022/data.
Nguyen, Quang. 2023. “Turn-Angle.” https://github.com/qntkhvn/turn-angle/blob/main/scripts/01a_prep_rusher_data.R.